opt-class: opt

In rtlemos/rcrandom: Pseudo-random number generators for random variables and vectors

Description

Optimize parameters and approximate probability density functions of random variables.

Details

Use objects of this class to optimize a p.d.f. and approximate it using products of independent, transformed parameters. You need to initialize an object of this class, call the constructor with a function and initial guesstimates for the unknown parameters, and finally call the set.z method. For convenience, you can do this in one step, when you initialize the object. Then, use the pdf method to obtain fast evaluations of the approximate p.d.f.

Fields

logpdf

Log-pdf to be optimized

npar

Number of unknown parameters

args

Other arguments required by log-pdf

iteration

Number of p.d.f. evaluations conducted

lower

Lower bounds for unknown parameters

upper

Upper bounds for unknown parameters

mode

Mode of pdf (par. value that maximizes pdf)

fmode

Maximum value of the log-pdf (value at mode)

lev0

Evaluation of the log-p.d.f. when pars = 0

covF

Covariance factor at the mode

precR

Precision factor at the mode

logdetPR

Log determinant of par. cov. at the mode

optim.res

Output from the optimization method

Z

List of transformed model parameters

Methods

cdf(x = NULL, ...)

Provides either cumulative density function or its evaluation given x

construct(fn, initial, is.logf = FALSE, lower = -Inf, upper = Inf, max.it = 300, args = NULL, zspecs = NULL, skip.z = FALSE, verbose = FALSE, method = "Nelder-Mead", optim.tol = 1e-04)

Optimization method that lets you find the mode of a p.d.f.

@param fn function p.d.f. (needn't integrate to 1) to be optimized

@param is.logf logical Is fn already log-transformed?

@param initial numerical Initial values for the p.d.f. parameters

@param lower numerical Lower bounds for the parameters

@param upper numerical Upper bounds for the parameters

@param args list Additional input arguments for the function

@param zspecs list Specifications used to transform the parameters

@param skip.z logical Should parameter transformation be skipped? @param method character Optimization algorithm @param optim.tol numerical Optimization relative tolerance

get.extremes(id)

Provides the bounds of the region where a given input parameter has non-zero density

get.x2z(x)

Provides transformed parameters based on original input parameters.

@param x numeric, matrix, Matrix X-coordinates to be transformed

@result z numeric, matrix, Matrix Transformed z-coordinates

get.z2x(z)

Provides parameters with their original units based on transformed parameters.

@param z numeric, matrix, Matrix Z-coordinates to be transformed

@result x numeric, matrix, Matrix Transformed x-coordinates

get.zaxis(id = 1)

Coordinates of transformed parameters, at all evaluation points.

@param id numeric Identification number of Z-axis

@result axis matrix X-coordinates of required Z-axis

iget.reshape(f, x = NULL)

Internal function that reshapes the input provided to pdf, cdf and invcdf

initialize(fn = NULL, initial = NULL, is.logf = FALSE, lower = -Inf, upper = Inf, max.it = 300, args = NULL, zspecs = NULL, skip.c = FALSE, skip.z = FALSE, verbose = FALSE, method = "GenSA", optim.tol = 1e-04)

Lets you run optimization and pdf exploration in one go

@param fn function p.d.f. (needn't integrate to 1) to be optimized

@param initial numerical Initial values for the p.d.f. parameters

@param is.logf logical Is fn already log-transformed?

@param lower numerical Lower bounds for the parameters

@param upper numerical Upper bounds for the parameters

@param args list Additional input arguments for the function

@param zspecs list Specifications used to transform the parameters

@param skip.z logical Should parameter transformation be skipped?

@param method character Optimization algorithm

@param optim.tol numerical Optimization relative tolerance.

invcdf(p = NULL, ...)

Provides either inverse of the cumulative density function or its evaluation, for a given p.

pdf(x = NULL, do.log = FALSE)

Approximate p.d.f. evaluation.

@param x numeric,matrix,NULL X-coords of points where pdf is evaluated

@param do.log logical Provide log-transformed p.d.f. instead?

@result myf numeric,matrix,function Either evaluations or R function

set.z(zspecs = NULL)

Provides transformed input parameters based on the optimization of the input function.

@param zspecs list list of specifications, e.g.

zspecs <- list(nside = 10, logtol = -5, eps = 1e-4,

useFortran = TRUE, useQuadratic = TRUE, useEigen = TRUE)

Examples

myfun <- function(x) dgamma(x, shape = 1.3, scale = 1) *
                     dnorm(x, mean = 2, sd = 1)
myfun.integ <- integrate(
             f = myfun, lower = 0, upper = 10)$value
fn <- function(x) myfun(x) / myfun.integ
s <- opt(fn = fn, initial = 1, lower = 0)
x <- seq(0, 10, 0.1)
plot(x, fn(x), ty = "l", col = "grey", lwd = 4,
   xlab = "x", ylab = "pdf")
lines(x, s$pdf(x))
legend(0.6 * max(x), max(fn(x)),
       c("true pdf", "rcoptim pdf"),
       col = c("grey", "black"), lty = 1)

rtlemos/rcrandom documentation built on May 28, 2019, 9:55 a.m.